Question

The area of the circle whose centre is (0, – 4) and passes through the point (–1, 5), is

Answer 1

Answer:

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Step-by-step explanation:

$so \: here \: for \: a \: certain \: circle \\ coordinates \: of \: its \: centre \: (h,k) = (0, - 4) \\ also \: it \: passes \: through \: points \: ( - 1,5) \\ so \: let \: (x,y) = ( - 1,5) \\ so \: now \: using \: centre \: radius \: form \: equation \: of \: circle \\ we \: get \\ (x - h) {}^{2} + (y - k) {}^{2} = r {}^{2} \\ = ( - 1 - 0) {}^{2} + (5 - ( - 4)) {}^{2} \\ = ( - 1) {}^{2} + (5 + 4) {}^{2} \\ = 1 + (9) {}^{2} \\ = 1 + 81 \\ = 82 \\ so \: \: r {}^{2} = 82$

$now \: we \: know \: that \\ area \: of \: circle \: = \pi.r {}^{2} \\ = \pi.82 \\ = 82\pi \\ hence \: area \: of \: circle = 82\pi \: unit {}^{2}$